debt valuation and interest

DEBT VALUATION AND INTEREST

Chapter 9

Principles Applied in This Chapter

Principle 1: Money Has a Time Value.

Principle 2: There is a Risk-Return Tradeoff.

Principle 3: Cash Flows Are the Source of Value

Corporate Borrowings

There are two main sources of borrowing for a corporation:

1. Loan from a financial institution (known as private debt since it involves only two parties)

2. Bonds (known as public debt since they can be traded in the public financial markets)

Borrowing Money in the Private Financial Market

Financial Institutions provide loans Working capital loans to finance firm’s day-to-day

operations Transaction loans for the purchase of equipment or

property Loans may or may not be secured by a collateral.

Table 9-1 Types of Bank Debt

Floating-Rate Loans

In the private financial market, loans are typically floating rate loans The interest rate is adjusted based on a specific

benchmark rate. The most popular benchmark rate is the London

Interbank Offered Rate (LIBOR), rate at which banks offer to lend in the London wholesale or interbank market

Floating-Rate Loans

For example, a corporation may get a 1-year loan with a rate of 300 basis points (or 3%) over LIBOR with a ceiling of 11% and a floor of 4%.

CHECKPOINT 9.1: CHECK YOURSELF

Calculating the Rate of Interest on a Floating-Rate Loan

Consider the same 1 yea loan periodCChange the spread over LIBOR from 75 basis points (00.75%). Is the ceiling rate or floor rate violated during the loan period?

Step 1: Picture the Problem (cont.)

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

1 2 3 4 5 6 7 8

Inte

rest

Rat

e

Floating Rate Loans

Series1

Series2

Series3

Series4

Step 2: Decide on a Solution Strategy

We have to determine the floating rate for every week and see if it exceeds the ceiling or falls below the floor. Floating rate on Loan

= LIBOR for the previous week + spread of .75%

The floating rate on loan cannot exceed the ceiling rate of 2.5% or drop below the floor rate of 1.75%.

Step 3: Solve

LIBOR LIBOR + Spread (.75%)

Loan Rate

2/29/2008 1.98%

3/7/2008 1.66% 2.73% 2.50%

3/14/2008 1.52% 2.44% 2.41%

3/21/2008 1.35% 2.27% 2.27%

3/28/2008 1.60% 2.10% 2.10%

4/4/2008 1.63% 2.35% 2.35%

4/11/2008 1.67% 2.38% 2.38%

4/18/2008 1.88% 2.42% 2.42%

4/25/2008 1.93% 2.63% 2.50%

5/2/2008 2.68% 2.50%

Ceiling Violated

Step 4: Analyze

If there were no ceiling, the loan rate would have been 2.73% during the first week of the loan, and 2.63% and 2.68% during the last two weeks of the loan. The rate was set to the ceiling of 2.50% for those three

weeks.

Corporate Bonds

Corporate bond is a debt security issued by corporation that has promised future payments and a maturity date.

If the firm fails to pay the promised future payments of interest and principal, the bond trustee can classify the firm as insolvent and force the firm into bankruptcy.

Basic Bond Features

The basic features of a bond include the following: Bond indenture Claims on assets and income Par or face value Coupon interest rate Maturity and repayment of principal Call provision and conversion features

Table 9.2 Bond Terminology

Table 9-7 Types of Corporate Bonds

Borrowing Money in the Public Financial Market

Corporations engage the services of an investment banker while raising long-term funds in the public financial market. The investment banker performs three basic functions:

Underwriting: assuming risk of selling a security issued. The client is given the money before the securities are sold to the public.

Distributing Advising

Table 9.3 Interpreting Bond Ratings

Valuing Corporate Debt

The value of corporate debt is equal to the present value of the contractually promised principal and interest payments (the cash flows) discounted back to the present using the market’s required yield to maturity on similar risk.


Step 1: Determine bondholder cash flows, which are the the amount and timing of the bond’s promised interest and principal payments to the bondholders.Annual Interest = Par value × coupon rateExample 9.1: The annual interest for a 10-year bond with coupon interest rate of 7% and a par value of $1,000 is equal to $70, (.07 × $1,000 = $70). This bond will pay $70 every year and $1,000 at the end of 10-years.


Step 2: Estimate the appropriate discount rate on a bond of similar risk.

Discount rate is the return the bond will yield if it is held to maturity and all bond payments are made.


Step 3: Calculate the present value of the bond’s interest and principal payments from Step 1 using the discount rate in step 2.

Calculating a Bond’s Yield to Maturity (YTM)

We can think of YTM as the discount rate that makes the present value of the bond’s promised interest and principal equal to the bond’s observed market price.


Calculating the Yield to Maturity on a Corporate Bond

Calculate the YTM on the Ford bond where the bond price rises to $900 (holding all other things equal).

• 11 year maturity• 6.5% coupon rate• $1000 face value

Step 1: Picture the Problem

YTM=?

YearsCash flow -$900 $65 $65 $65 $1,065

Purchase price = $900 Interest payments = $65 per year for years 1-11 Final payment = $1,000 in year 11 of principal.

0 1 2 3 … 11


YTM is the solution to

Step 3: Solve

Using a Financial CalculatorNeed to find interest rateN = 11 PV = -90PMT = 65FV = 1,000 I/Y = 7.89

Step 4: Analyze

The yield to maturity on the bond is 7.89%. The yield is higher than the coupon rate of interest of

6.5%. Since the coupon rate is lower than the yield to

maturity, the bond is trading at a price below $1,000. We call this a discount bond.

Table 9-4 Corporate Bond Credit Spread Tables

Promised versus Expected Yield to Maturity

The yield to maturity calculation assumes that the bond performs according to the terms of the bond contract or indenture. Since corporate bonds are subject to risk of default, the promised yield to maturity may not be equal to expected yield to maturity.

That is, we need to take account of the default risk in our YTM calculation


Example Consider a one-year bond that promises a coupon rate of 8% and has a principal (par value) of $1,000. Further assume the bond is currently trading for $850.

Promised YTM

= {(Interest year 1 + Principal) ÷ (Bond Value)} – 1= {($80+$1,000) ÷ ($850)} – 1 = 27.06%


Assume there is a 40% probability of default on this bond

If the bond defaults, the bondholders will receive only 60% of the principal and interest owed. What is the expected YTM on this bond?

YTMdefault

= {(Interest year 1 + Principal)} ÷ (Bond Value)} – 1= {($80+$1000) × .60} ÷ ($850)} – 1= -23.76%


Valuing a Bond Issue

Calculate the value of the AT&T bond should the yield to maturity for comparable risk bonds rise to 9% (holding all other things equal).


i= 9%

Years

Cash flows $85 $85 $85 $1,085

0 1 2 3 … 20

PV of allCash flows =?

$85 annualinterest $85 interest

+ $1,000 Principal


Here we know the following: Annual interest payments = $85 Principal amount or par value = $1,000 Time = 20 years YTM or discount rate = 9%

We can use the above information to determine the value of the bond by discounting future interest and principal payment to the present.

Step 3: Solve

Using a Mathematical Formula

= $ 85{[1-(1/(1.09)20] ÷ (.09)}+ 1,000/(1.09)20

= $85 (9.128) + $178.43= $954.36

Step 3: Solve

Using a Financial Calculator

N = 20 I/Y = 9.0 PMT = 85 FV = 1000 PV = 954.36

Step 4: Analyze

The value of AT&T bond falls to $954.36 when the yield to maturity rises to 9%. The bonds are now trading at a discount as the coupon rate on AT&T bonds is lower than the market yield.

An investor who buys AT&T bonds at its current discounted price will earn a promised yield to maturity of 9%.

Semiannual Interest Payments

Corporate bonds typically pay interest to bondholders semiannually.


Valuing a Bond Issue That Pays Semiannual Interest

Calculate the present value of the AT&T bond should the yield to maturity on comparable bonds rise to 9% (holding all other things equal).


i= 9%Periods

Cash flow

$42.5 42.5 $42.5 $1,042.50

0 1 2 3 … 40

PV=?

$42.50 Semiannualinterest

$42.5 interest + $1,000 Principal

40 6-monthperiods


Here we know the following: Semiannual interest payments = $42.50 Principal amount or par value = $1,000 Time = 20 years or 40 periods YTM or discount rate = 9% or 4.5% for 6-months

We can use the above information to determine the value of the bond by discounting future interest and principal payment to the present.

Step 3: Solve

Using a Mathematical Formula

= $ 42.5{[1-(1/(1.045)40] ÷ (.20)} + $1,000/(1.045)40

= $42.5 (18.40) + $171.93= $953.996

Step 3: Solve

Using a Financial Calculator

N = 40 1/y = 4.50 PMT = 42.50 FV = 1000 PV = 953.996

Step 4: Analyze

Using semi-annual compounding we get a value of $953.9960 for AT&T bonds. This is very close to the value of $954.36 found using annual compounding.

Bond Valuation: Four Key Relationships

First Relationship The value of bond is inversely related to changes in the yield to maturity.

YTM = 12% YTM rises to 15%

Par value $1,000 $1,000Coupon rate 12% 12%Maturity date 5 years 5 yearsBond Value $1,000 $899.44

Bond Value Drops

Figure 9-1 Bond Value and the Market’s Required Yield to Maturity (5-Year Bond, 12% Coupon Rate)


Second Relationship: The market value of a bond will be less than the par value (discount bond) if the market’s required yield to maturity is above the coupon interest rate and will be valued above par value (premium bond) if the market’s required yield to maturity is below the coupon interest rate.


Third Relationship As the maturity date approaches, the market value of a bond approaches its par value. That’s because at maturity the bond will be taken away

and the investor will receive the par value of the bond.

Figure 9-2 Value of a 12% Coupon Bond during the Life of the Bond


Fourth Relationship Long term bonds have greater interest-rate risk than short-term bonds. While all bonds are affected by a change in interest

rates, the prices of longer-term bonds fluctuate more when interest rates change than do the prices of shorter-term bonds (see Table 9.6)

Determinants of Interest Rates

As we observed earlier, bond prices vary inversely with interest rates.

Therefore in order to understand how bond prices fluctuate, we need to know the determinants of interest rates.

Inflation and Real versus Nominal Interest Rates

Quotes of interest rates in the financial press are commonly referred to as the nominal (or quoted) interest rates.

Real rate of interest adjusts for the effects of inflation.

Fisher Effect: The Nominal and Real Rate of Interest

The relationship between the nominal rate of interest, rnominal , the anticipated rate of inflation, rinflation , and the real rate of interest is known as the Fisher effect.

1+ rnominal = (1+ rreal)(1+ rinflation) = 1+rreal +rinflation +rreal*rinflation

≈ 1+ rreal + rinflation

Interest Rate Determinants

We can think of the reported nominal = interest rate on a bond as having five components: Real risk-free rate The inflation premium Default–risk premium Maturity-risk premium Liquidity-risk premium

The Maturity-Risk Premium and the Term Structure of Interest Rates

The relationship between interest rates and time to maturity with risk held constant is known as the term structure of interest rates or the yield curve.

Figure 9-3 illustrates a hypothetical term structure of U.S. Treasury Bonds.

Figure 9-3 The Term Structure of Interest Rates or Yield Curve

The Shape of the Yield Curve

By reviewing equation 9-5, we can gain insight into the shape of the yield curve for US Treasuries. Since there is no default risk or liquidity risk and the real-risk free rate of interest is unlikely to change, the shape of the yield curve is driven by inflation premium and maturity risk premium.

The Shape of the Yield Curve

During periods when inflation is expected to subside, the inflation premium should decrease over longer maturities, resulting in a downward sloping Treasury yield curve as shown in Figure 9.5. The reverse is also true as shown in Figure 9.4

Figure 9.4 Treasury Yield Curve during Period of Increasing Inflation

Figure 9.5Treasury Yield Curve during Period of Decreasing Inflation

Shifts in the Yield Curve

The yield curve changes over time as expectations regarding each of the four factors that underlie interest rates change.

Figure 9-6 shows the yield curve one day before 911 attack and again two weeks later. Investors shifted their funds to the safety of Treasuries, pushing up the prices and bringing down the yields.

Figure 9-6 Changes in the Term Structure of Interest Rates around September 11, 2001

Shifts in the Yield Curve

The yield curve is generally upward sloping but it can assume different shapes i.e. downward sloping or flat.

Figure 9-7 illustrates different shapes of yield curves at different dates, observed within a span of only 13 months.

Figure 9.7 Historical Term Structure of Interest Rates for Government Securities

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